Stylistic Automata in "Gradient"

Along with comparative search, the automated techniques used to compose Gradient include two additional approaches: constrained search and sorting. Comparative search, constrained search, and sorting provide judicious solutions to compositional problems that involve some collection of entities (e.g., sections, chords, notes) and that attempt to select an attribute (e.g., durations, registers, pitches) for each entity. In describing these techniques, it will be convenient to refer to individual acts of selection as decisions and to refer to a collection of decisions, one for each entity, as a solution to a problem. In a comparative search, the computer compares many different solutions in order to discover the solution in greatest accord with a protocol (i.e., a ranked collection) of directives established by the composer. This technique derives historically from Claude Shannon's algorithms for playing chess by computer (1950). I have discussed comparative search extensively in my article on Protocol (1981). A constrained search seeks a solution conforming to one or more strict rules, again provided by the composer. Whenever a constrained search encounters some decision in which no option satisfies all of these rules, the search backtracks, revises one or more earlier decisions, and tries again. Constrained searches are much faster than comparative searches, but only produce acceptable solutions, not optimal ones. They have the disadvantage that since all constraints are absolute, one cannot rank them. The composer can, however, supply heuristics controlling the order in which the computer schedules options for each decision. Since a constrained search accepts the first solution it finds, such heuristics will bias this solution toward tendencies which, though desirable, do not merit absolute status as constraints. Constrained search is a basic technique of artificial intelligence (Nilsson 1971). It was first applied to musical problems by Stanley Gill (1963), but languished until its revival as a theoretic tool by my colleague Kemal Ebcioglu (1981). Sorting can be used to solve compositional problems when all of the attributes are drawn from a